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Emergent spacetime and the ergodic hierarchy
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abstract
Various diagnostics of the emergence of an arrow of time in the bulk description of a holographic theory have been proposed, including the decay of some real time correlation functions and the appearance of type III$_1$ von Neumann algebras carrying half-sided modular inclusions. This note puts forward a close parallel between these diagnostics and a quantum formulation of the ergodic hierarchy of dynamical systems. Theories with an emergent spacetime appear to sit near the top of this hierarchy.
Forward citations
Cited by 3 Pith papers
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Chaos and the Emergence of the Cosmological Horizon
Finite-mass observers in dS2 have non-commuting type I algebras, and their OTOC shows a Lyapunov exponent 4π/β_dS, twice the de Sitter bound.
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Type III von Neumann Algebras are Magical
If lattice states in the thermodynamic limit have bounded magic, the local von Neumann algebra cannot be Type III, so Type III algebras require infinite magic.
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Black holes from chaos
Chaotic thermal correlators can be computed by mapping Lanczos coefficients to a black-hole scattering problem, giving quasinormal-mode resonances from short-time data.
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